Steady Viscous Flow Past a Circular Cylinder up to Reynolds Number 600

The inspiring review oflaminar separation by Brown & Stewartson (1969) begins thus: "The phenomenon of separation is one of the most interesting features of the motion of an incompressible fluid past a bluff body at high Reynolds number. Here the main stream, which has hitherto been in close contact with the body, suddenly, and for no obvious reason, breaks away, and downstream a region of eddying flow, which is usually turbulent even if the flow elsewhere is laminar, is set up." These opening lines-which were followed by the above authors' brilliant and timely discourse emphasizing the difficulties associated with separation in classical boundary layers­ make an apt beginning for the present article on the current state of the art. The main feature, to which Brown & Stewarts on in fact alluded strongly, is that given the failure [due to singularities of the S. Goldstein (1948) type] in classical theory at separation, a fresh nonclassical start is necessary for high-Reynolds-number theory to encompass separating flow. This start was made by Stewartson & Williams (1969), Neiland (1969), and Messiter (1970). Our aim is to go from the significant advances made since 1969 to the recent developments and the possible areas of progress in the near future for the rational theory 'of steady and unsteady separation. The physical and theoretical understanding that can emerge from the study of flow structures at large characteristic Reynolds numbers Re is valuable for many reasons. Three major ones are the helpful comparisons with experiments and numerical results, the foundation such study gives to

Steady and Unsteady Boundary-Layer Separation

Low frequency pressure oscillations in a research ramjet combustor have been studied using an integral technique. The analysis deals with plane one-dimensional oscillations with a two-dimensional mean flowfield. The flowfield in the dump combustor consists of three parts: a flow of reactants, a region containing combustion products, and a recirculation zone. separated by a flame sheel and a dividing streamline. Each region is treated separately and matched with the other. Acoustic fields in the inlet section and in the combustion chamber are coupled at the interface to determine the complex wave number characterizing the linear stability. Good agreement with experimental results has been demonstrated.

Analysis of Low Frequency Combustion Instabilities in a Laboratory Ramjet Combustor

Review of the physics of enhancing vortex lift by unsteady excitation

The nonlinear instability of Hill's spherical vortex, subject to axisymmetric perturbations is considered. The problem is formulated as a nonlinear integrodifferential equation for the motion of the vortex boundary. This equation is solved employing a numerical procedure which involves a piecewise representation of the vortex contour with discrete elements. This formulation offers an efficient method for studying a variety of vortex flows in axisymmetric geometry.Our results indicate that if Hill's vortex becomes a prolate spheroid, a certain amount of rotational fluid is detrained from the rear stagnation point of the vortex, leaving behind a reduced vortex of approximately spherical shape. The amount of detrained fluid is a function of the initial deformation. If the vortex becomes an oblate spheroid, irrotational fluid is entrained into the vortex from the rear stagnation point, reaches the front vortex boundary, and circulates along the vortex boundary in a spiral pattern. In this fashion, the vortex reduces to a nearly steady vortex ring whose asymptotic structure is a function of the initial deformation. The structure of the asymptotic rings arising from oblate vortices is similar to that of steady rings described by Norbury (1973). The vortex speed is shown to tend to a constant value for prolate perturbations, and to fluctuate around a mean value for oblate perturbations.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S002211208600040X

The nonlinear instability of Hill's vortex

Two-dimensional steady inviscid flow past an inclined flat plate with a forward-facing flap attached to the rear edge is considered for the case when a vortex sheet separates from the leading edge of the flat plate and reattaches at the leading edge of the flap, with uniform vorticity distributed between the vortex sheet and the body. Solutions are found for a particular geometry and a range of values of the vorticity. The method used to calculate the flow is an extension of a free-streamline method widely used in cases where the velocity is a constant on the separating streamline.

/pdf/prandtl-batchelor-flow-past-a-flat-plate-with-a-forward-4epvhvldn3.pdf

S. Tanveer

Papers

Prandtl–Batchelor flow past a flat plate with a forward-facing flap